The trouble with Jay Bouwmeester is that nobody knows for certain what he is — other than available.

We do know that no matter who he is, no matter where he signs after July 1, that he will be made extraordinarily wealthy. What we can’t say for certain, and so many hockey people are guessing about it, is whether he becomes the next dominant defenceman in hockey or the next terrible contract a la Bryan McCabe or Wade Redden.

Brian Burke can’t admit to the possibility of being intrigued by Bouwmeester because that would constitute tampering eight days before the free agent season officially begins. But he is thinking about it. He is thinking seriously about this 25-year-old defenceman. And the Maple Leafs will be among the bidders on July 1, no matter how silent he remains for now.

Just how high they are willing to go, how much money, how many years — and whether Bouwmeester would have any interest in playing in Toronto for a team on the rebuild — are all questions in need of answers for a player who has yet to define his career.

The Leafs, being where they are, have no choice but to take a shot at Bouwmeester. Because of his age. Because of his size. Because of his skill set. Because of all the possibilities he presents. Look how Zdeno Chara helped turn around a Boston Bruins team in terrible shape. Could Bouwmeester have the same kind of impact where he eventually lands?

Denis Potvin, who knows defencemen, isn’t certain. He has watched every game of Bouwmeester’s career as a former broadcaster with the Panthers, and is stuck for an answer when asked how great a player Bouwmeester is, and more importantly, how great he will be.

“In my view, what Jay has not shown yet is the ability to really control the game, the way a No. 1 defenceman should be able to,” said Potvin, a Hall of Fame defender who could control a game. “Now that could change if he ends up going to a team that’s a contender and surrounds him with better players. At times, he looks like he wants to control the game, but I don’t know if he knows how to do it.

“And, do you want to pay all that money, $7 million a year or more, for a guy who might not be a No. 1 defenceman?”

Canadiens general manager Bob Gainey took some time out to receive an award on behalf of the Canadiens last night, but fans can rest assured that he’s busily preparing for next season.

Gainey graced the head table as the Canadian Association of New York saluted the Canadiens’ centenary at their annual hockey achievement award dinner at the Waldorf-Astoria Hotel.

But Gainey spent some time earlier in the day talking to some of the team’s unrestricted free agents.

“We’ve had some preliminary discussions, but I told them that we’re not going to make any moves until after the draft,” Gainey said, offering the tantalizing possibility that the team may pull off a blockbuster deal during the weekend.

Gainey did say there has been some movement on the coaching front, but the big news is who’s going.

Last week, he told Don Lever and Ron Wilson their services were no longer needed. They were the guiding force behind the Hamilton Bulldogs in recent years and Lever was called up to the Canadiens to provide the younger players with a comfort level after Gainey fired Guy Carbonneau.

There was speculation in the spring that fluency in French was the only thing standing between Lever and the head coaching job in Montreal, but Lever should have figured his future was limited when Gainey gave him permission to talk with other teams.

Gainey also announced that Doug Jarvis, who held the title of associate coach will not return to the team. Kirk Muller will be back and Gainey said new head coach Jacques Martin is still working on filling out his staff.

Red Wings defenseman Chris Chelios is slated to meet with general manager Ken Holland in the next few days to talk about his future.

Chelios, the league’s oldest active player at 47, didn’t talk to reporters after the annual team photo last week. He had declined to talk about his future during the playoffs, but made it known he wanted to continue to play.

Holland said he had a good talk with Chelios when they were on the same flight to Las Vegas last week to attend the NHL awards.

Chelios was among the players attending a meeting with NHL commissioner Gary Bettman on Saturday in Vegas, but did not return calls from the Free Press seeking comment. Although he has been critical of Bettman in the past, Chelios told the Canadian Press on Saturday that it was a respectful meeting.

“We weren’t going to do anything that was unprofessional,” Chelios said. “It took a lot for him to go out of his way and address the players. I just wish we had 700 guys in here to listen to him.”

Dany Heatley has told the Ottawa Senators where he wants to go. But if the Senators can’t trade him before a $4-million US bonus kicks in on July 1, they may tell him where to go.

Senators general manager Bryan Murray expects talks will heat up this week at the NHL draft in Montreal as several league sources confirmed Heatley’s agents have given the club a wish list of up to 10 teams. But there could be some flexibility — he may agree to go somewhere not listed.

While the Red Wings and Bruins likely would have a difficult time making a move under the $56.7-million salary cap, it’s believed discussions have been held with the Kings, Rangers, Sharks and Canucks.

Sources say Minnesota, Colorado, Edmonton and St. Louis are taking a serious look as well.

The Kings could make a deal with the $7.5 million in cap space by offering up defenceman Jack Johnson and forward Alexander Frolov.

The Oilers want to bring in a big-time winger such as Heatley, but sources have confirmed he wasn’t on the list submitted to Murray.

“I’m doing a lot of the asking. Nobody has really agreed at the moment. But one team is getting close to where I want to be,” Murray said at a pre-draft media availability yesterday at Scotiabank Place. “I guess I can take an offer that has been made, but it’s not one that I want right now.”

Senators owner Eugene Melnyk doesn’t want to be on the hook for the $4-million bonus.

If Heatley isn’t gone before July 1, he could be back with the Senators next season.